Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery -- possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput -- a decision that should be influenced by the device's physical noise.

翻译：运行受量子纠错保护的量子算法需要实时的经典解码器。为防止任务积压，该解码器必须以快于量子设备生成速度的速率处理综合征。此前关于实时解码的研究主要集中在表面码中孤立逻辑量子比特的解码。然而，对于表面码而言，实用量子程序需要通过晶格手术实现多量子比特相互作用。在晶格手术过程中可能出现大型合并补丁——其规模可能覆盖整个设备。这给实时解码器带来显著压力：它必须解码该合并补丁上的错误，同时维持孤立逻辑量子比特所达到的容错水平。通过采用空间并行解码可缓解这些要求，具体方法是将设备上的物理量子比特划分为多个重叠组，并为每组分配一个解码器模块。我们将此方法称为空间并行窗口。尽管此前研究探讨过类似思路，但均未涉及与任务相关的系统特性考量，也未涉及硬件加速器的约束条件。本研究展示了如何配置空间并行窗口，使该方案：（1）与硬件加速器兼容，（2）支持通用晶格手术操作，（3）维持逻辑量子比特的保真度，（4）满足实时解码的吞吐量要求。此外，我们的结果揭示了最优缓冲区宽度选择的重要性——需在精度与吞吐量间取得平衡，且此决策应受设备物理噪声特性的影响。